Motivated by a problem arising in astrophysics we study a nonlinear elliptic equation in with cylindrical symmetry and with singularities on a whole subspace of . We study the problem in a variational framework and, as the nonlinearity also displays a critical behavior, we use some suitable version of the Concentration-Compactness Principle. We obtain several results on existence and nonexistence of solutions.
Cite this article
Marino Badiale, Enrico Serra, Critical nonlinear elliptic equations with singularities and cylindrical symmetry. Rev. Mat. Iberoam. 20 (2004), no. 1, pp. 33–66DOI 10.4171/RMI/379